Let us solve the following linear simultaneous equations in two variables by the method of elimination:

Rewriting the above equation as.

x + y = 5xy (i)

x - y = 9xy (ii)

In this problem, we will eliminate ‘y’ from both the equations.

Adding both the equations

2x = 14xy (cancelling x from both the sides)

⇒

Putting the value of y in equation(i)

x = 5xy - y or x = - 1/2

Hence the solution of the linear equation is x = and y = -1/2

Note: - Since we have cancelled x as it is common from both the sides, we have neglected a solution that is x = 0, similarly other solution as y = 0.